Internal Rate of Return (IRR) Calculator
The Discount Rate Where a Project Breaks Even
Internal rate of return is the discount rate at which a project's net present value equals exactly zero — the rate at which the present value of future cash flows exactly offsets the initial investment. There's no closed-form formula that solves for it directly for most cash flow patterns, so this calculator finds it numerically, narrowing in on the rate through repeated bisection until the resulting NPV is effectively zero.
The Formula
The cash flow at t=0 is the negative initial investment; each subsequent cash flow is discounted by (1 + r) raised to its year number. The calculator brackets a root by scanning a range of rates for a sign change in NPV, then bisects repeatedly until it converges.
Where This Matters
- Comparing project returns directly — IRR expresses a project's return as a single percentage, making it easy to compare against a hurdle rate or against other investment opportunities.
- Setting a hurdle rate test — a common capital budgeting rule is to accept a project only if its IRR exceeds the company's cost of capital, since that means it generates value above what the capital actually costs.
- Private equity and venture return reporting — IRR is a standard performance metric quoted for funds and individual deals precisely because it accounts for the timing, not just the total size, of cash flows.
Worked Example
The same cash flow schedule used for the NPV example — a $10,000 initial investment returning $3,000, $4,000, $4,000, and $3,000 over four years — produces an IRR of 14.90%. This is the rate at which those cash flows, discounted, exactly cover the $10,000 initial cost.
| Year | Cash flow |
|---|---|
| 0 (initial investment) | -$10,000 |
| 1 | $3,000 |
| 2 | $4,000 |
| 3 | $4,000 |
| 4 | $3,000 |
At an 8% discount rate this same schedule produced a positive NPV of $1,587.55, consistent with an IRR (14.90%) above the 8% discount rate — NPV is positive whenever the discount rate is below the IRR.
How to Use This Calculator
- Enter the initial investment (upfront cost).
- Enter the future cash flows, comma-separated, in order (e.g.
3000,4000,4000,3000). - Select Calculate to get the internal rate of return.
Related Calculations
Compare IRR against a specific required return with the Net Present Value (NPV) Calculator, or see how quickly the investment recovers with the Payback Period Calculator.